Selection of Background and Foreground Pixels: In order to train the localization map predictor, a pixel-level supervisory signal is employed. At each epoch, new pseudo-labels are generated that consist of few foreground and background pixels (pseudo-pixels) to increase network certainty of different regions during training. To select pseudo-pixels, we extract attention maps from the last layer of the transformer, corresponding to class tokens. From the maps, we select only the first four maps and an average map of all class tokens. After this, we apply the Otsu [1]} thresholding method for converting the attention map into a binary map to obtain all connected regions that are greater than a minimum sizeThe minimum size is an hyperparameter value. to extract all \(B\)  proposal (bounding) boxes enclosing those regions. Then, for an input image, we produce \(B\)  images corresponding to each bounding box by applying the Gaussian-blur filter to hide the background regions outside of the respective bounding box. Each image is then passed to a classifier \(\mbox{\sbox {}{$\mathrm {C}$}\hspace{0.0pt}{1 0 .3 1}\unknown. {\usebox {}}}\) , and the top P best proposals along with their underlying attention maps are selected based on the classifier's confidence corresponding to target class \(\mathrm {y}_i\) . Then, one out of P proposals along with its respective bounding box is selected for pseudo labeling. The pixels inside and outside of the bounding box are considered as foreground 1 0 .3 1\(\mathbb {Y}_i^+\) and background regions 1 0 .3 1\(\mathbb {Y}_i^-\) respectively defined as:
\(\mbox{\sbox {}{$\mathbb {Y}_i^+$}\hspace{0.0pt}{1 0 .3 1}\unknown. {\usebox {}}}=\varphi ^+(Y_i,n^+) \quad \quad \quad \mbox{\sbox {}{$\mathbb {Y}_i^-$}\hspace{0.0pt}{1 0 .3 1}\unknown. {\usebox {}}}=\varphi ^-(Y_{i},n^-)\) 
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